1. 5.2: Writing Linear Equations Given the Slope and a Point
Homework 42: p.282: 13-29, 33-39, All
Learning Objectives:
Use the slope and any point on a line to write an equation of the line
Find the slope of the line containing each pair of points.
(0, 2) and (3, 4)
(–2, 8) and (4, 2)
(3, 3) and (12, –15)
𝒎= 𝟐 𝟑
𝒎=−𝟏
𝒎=−𝟐

2. Concept: The Ordered Pair
(𝑥,𝑦)
𝑦=𝑚𝑥+𝑏

3. Example 1: The Slope and an Ordered Pair
Write an equation with the slope of −2 that passes through (6, −3)
𝑦= 𝑚 𝑥 + 𝑏 𝑦 −3 𝑚 −2 𝑥 6
−3=−12+𝑏
9=𝑏

4. Example 1: The Slope and an Ordered Pair
Write an equation with the slope of −2 that passes through (6, −3)
9=𝑏
𝑦= 𝑚𝑥+𝑏
𝑦= 𝑚𝑥+𝑏 −2 9

5. Example 1: The Slope and an Ordered Pair
Step 1:
Substitute the slope in for 𝑚, the x-coordinate for 𝑥 and the y-coordinate for 𝑦
𝑚=−2, (6,−3)
𝑦=𝑚𝑥+𝑏
−3=−2 6 +𝑏
Solve the equation for 𝑏
Step 2:
−3=−2 6 +𝑏
−3=−12+𝑏
9=𝑏
Substitute 𝑚 and 𝑏 leaving 𝑥 and 𝑦 as variables
Step 3:
𝑦=−2𝑥+9

6. Student Led Example 1: The Slope and a Point
Write an equation, in Slope Intercept Form given a point and a slope
𝑦=3𝑥+3 A
−1,0 , 𝑚=3 B
3,6 , 𝑚=0
𝑦=6
𝑦=− 1 4 𝑥−2
4,−3 , 𝑚=− 1 4 C
𝑦= 1 2 𝑥+4
2, 5 , 𝑚= 1 2 D

7. Concept: Parallel Lines
Parallel lines are lines in the same plane that have no points in common. In other words, they do not intersect.
Parallel lines
HAVE.
EQUAL.
SLOPES.

8. Example 3: Writing an Equation for a Parallel Line
Write an equation parallel 𝒚= 𝟏 𝟐 𝒙−𝟒 that passes through the point (𝟐, 𝟓)
𝒎= 𝟏 𝟐
Step 1: Identify the Slope
Step 2: Use the Slope and Given Point
𝟓= 𝟏 𝟐 𝟐 +𝒃
𝒃=𝟒
Step 3: Find 𝒃
𝒚= 𝟏 𝟐 𝒙+𝟒
Step 4: Write the Equation

9. Student Led Example 3: Parallel Lines
Write an equation parallel to the given equation through the given point:
Given Equation: Given Point: Answer:
𝒚=𝟑𝒙−𝟒 (𝟎, 𝟒)
𝒚= 𝟏 𝟑 𝒙−𝟐 −𝟔, −𝟑
𝒙=𝟎 (𝟒, 𝟕)
𝒚=𝟑𝒙+𝟒
𝒚= 𝟏 𝟑 𝒙−𝟏
𝒙=𝟒

10. End of Lesson
Exit Task
Between 2012 and 2016, the monthly rent for a one- bedroom apartment in Portland increased by $120 a year. In 2014, the average rent was $900 per month.
Find an equation that gives the monthly rent in dollars, 𝑦, in terms of the year, 𝑡. Let 𝑡=0 correspond to
Determine the average rent in 2018.

11. End of Lesson
Between 2012 and 2016, the monthly rent for a one-bedroom apartment in Portland increased by $120 a year. In 2014, the rent was $900 per month.
Find an equation that gives the monthly rent in dollars, 𝑦, in terms of the year, 𝑡. Let 𝑡=0 correspond to 2012.
Determine the average rent in 2018.
Slope: =30
Intercept: in 2012, the rent is $900−2(30)=$840
2012: 𝑦=30𝑥+840
2018: 𝑦= =$1020